If you have a camper, you can search for a place at Køge to spend the night here.
Motorhomes are very welcome to park in specially designed pitches, which are close to the beach and harbor baths. You can park here for max. 1 day. The motorhome area is open in June, July and August. See more info here.
If you are going further out in Denmark, you can find a place to spend the night with your motorhome here.